Transient dynamics in the thermal ratchets transport model

The thermal ratchets model toggles a spatially periodic asymmetric potential to rectify random walks and achieve transport of diffusing particles. We numerically solve the governing equation for the full dynamics of an infinite 1D ratchet model in response to periodic switching. Transient aperiodic behavior is observed that converges asymptotically to the period of the switching. We study measures of the transport rate, the transient lifetime, and an equivalent of `amplitude', then investigate their dependence on various properties of the system, along with other features of the transient and asymptotic dynamics.